- Position: PhD Student -
- Principal supervisor: Dr Xian Zhou
- Date of submission: 01/01/2014
- Thesis title: On the time-inconsistent investment and dividend problems
- Abstract: We consider the time-inconsistent control problems. First, we study the mean-variance asset-liability management with state-dependent risk aversion. By solving a flow of FBSDEs with bivariate state process, we obtain the equilibrium strategy among all the open-loop controls for this time-inconsistent control problem. Second, we consider the dividend strategies for a shareholder with non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to the Markov strategies. The extended HJB equation is given and the verification theorem is proved for a general discount function. Considering the pseudo-exponential discount functions, we get the equilibrium dividend strategies and the equilibrium value functions.